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Find the number of solution of the equat...

Find the number of solution of the equation
`x^(3)+2x+cosx+tanx=0 in (-(pi)/(2),(pi)/(2))`

Text Solution

Verified by Experts

The correct Answer is:
one solution
Let f(x) =`x^(3)+2x+cos x +tan x`
`therefore f(x) =3x^(2)+(2-sinx)+sec^(2)xgt0`
So f(x) is incresing funciton
`therefore f(x) =1 and f(-1)lt0`
Therefore equation has one solution in `((pi)/(2),(pi)/(2))`
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